Digital Signal Processing Reference
In-Depth Information
It can be concluded that the experimental results fit the theoretical noise level
fairly well. Note that the actual measured noise level is slightly higher than
the theoretical noise value. This deviation can be accounted to the thermal
channel noise of the input pair in the first stage of the vga, which was ignored
in the above analysis. Note that the capacitance used in (6.1) does not only
include the physical capacitor at the output of the mixer (630 fF), but also the
output impedance of the mixer and the load of the vga (
120 fF). One way
to reduce the equivalent input noise of the baseband amplifier is to increase
the transimpedance of the first input stage by increasing the width of the input
pair. The higher load from the input pair must be compensated by a smaller
capacitor at the output of the mixer. Remark that it is not a good idea to replace
the entire physical capacitor by the capacitive load of the vga. The underlying
problem is that the parasitic capacitance between the differential inputs of a
differential cmos transistor pair has a parasitic capacitance to ac-ground, due
to the drain capacitance of the current transistor at the common source node.
For high frequency components in output current of the mixer (above the cut-
off frequency of the baseband amplifier), this would imply that the mixer is
loaded by two grounded capacitors, which would destroy the benefits of a fully
differential architecture.
The only thing left over to specify is the
noise figure
of the analog front-end.
For this, let us first define the
noise factor
of a component in a system. The
noise factor (f) is defined as the ratio between the snr of the signal at the
input versus the remaining snr value at its output. Since a circuit block can
only add noise to a signal, the noise factor is always larger than unity. When
the noise factor is expressed in decibels, it is referred to as the noise figure (nf)
of the system (6.2):
≈
snr
in
snr
out
f
>
1
nf
10 log
10
(
f
) >
0 dB
(6.2)
Earlier in this section, it was pointed out that the input stage does not offer any
active gain, since the rf input signal is directly injected into the mixer input
lines. This was done to achieve wideband input matching and to obtain a high
linearity of the input stage. For a system block without active gain, the formula
of the noise factor merely reduces to a ratio between noise power levels (6.3):
s
in
/
n
in
s
out
/
n
out
=
n
out
n
in
=
n
in
+
n
system
n
in
f
[no gain]
=
(6.3)
It follows that in absence of interference, the thermal background noise cap-
tured by the antenna is the only factor that contributes directly to the input
noise of the system. For example, when the rf input bandwidth of the receiver
